Generalization of a Theorem on Eigenvalues of Symmetric Matrices
Rohn, Jiří
2019 - anglický We prove that the product of a symmetric positive semide nite matrix and a symmetric matrix has all eigenvalues real. Klíčová slova: symmetric matrix; positive semide nite matrix; real spectrum Plné texty jsou dostupné v digitálním repozitáři NUŠL Generalization of a Theorem on Eigenvalues of Symmetric Matrices

We prove that the product of a symmetric positive semide nite matrix and a symmetric matrix has all eigenvalues real.

Rohn, Jiří
Ústav informatiky, 2019

Hybrid Methods for Nonlinear Least Squares Problems
Lukšan, Ladislav; Matonoha, Ctirad; Vlček, Jan
2019 - anglický This contribution contains a description and analysis of effective methods for minimization of the nonlinear least squares function F(x) = (1=2)fT (x)f(x), where x ∈ Rn and f ∈ Rm, together with extensive computational tests and comparisons of the introduced methods. All hybrid methods are described in detail and their global convergence is proved in a unified way. Some proofs concerning trust region methods, which are difficult to find in the literature, are also added. In particular, the report contains an analysis of a new simple hybrid method with Jacobian corrections (Section 8) and an investigation of the simple hybrid method for sparse least squares problems proposed previously in [33] (Section 14). Klíčová slova: numerical optimization; nonlinear least squares; trust region methods; hybrid methods; sparse problems; partially separable problems; numerical experiments Plné texty jsou dostupné v digitálním repozitáři NUŠL Hybrid Methods for Nonlinear Least Squares Problems

This contribution contains a description and analysis of effective methods for minimization of the nonlinear least squares function F(x) = (1=2)fT (x)f(x), where x ∈ Rn and f ∈ Rm, together with ...

Lukšan, Ladislav; Matonoha, Ctirad; Vlček, Jan
Ústav informatiky, 2019

Does a Singular Symmetric Interval Matrix Contain a Symmetric Singular Matrix?
Rohn, Jiří
2019 - anglický We consider the conjecture formulated in the title concerning existence of a symmetric singular matrix in a singular symmetric interval matrix. We show by means of a counterexample that it is generally not valid, and we prove that it becomes true under an additional assumption of positive semide niteness of the midpoint matrix. The proof is constructive. Klíčová slova: symmetric interval matrix; singularity; positive semide niteness Plné texty jsou dostupné v digitálním repozitáři NUŠL Does a Singular Symmetric Interval Matrix Contain a Symmetric Singular Matrix?

We consider the conjecture formulated in the title concerning existence of a symmetric singular matrix in a singular symmetric interval matrix. We show by means of a counterexample that it is ...

Rohn, Jiří
Ústav informatiky, 2019

Transforming hierarchical images to program expressions using deep networks
Křen, Tomáš
2018 - anglický We present a technique describing how to effectively train a neural network given an image to produce a formal description of the given image. The basic motivation of the proposed technique is an intention to design a new tool for automatic program synthesis capable of transforming sensory data (in our case static image, but generally a phenotype) to a formal code expression (i.e. syntactic tree of a program), such that the code (from evolutionary perspective a genotype) evaluates to a value that is similar to the input data, ideally identical. Our approach is partially based on our technique for generating program expressions in the context of typed functional genetic programming. We present promising results evaluating a simple image description language achieved with a deep network combining convolution encoder of images and recurrent decoder for generating program expressions in the sequential prefix notation and propose possible future applications. Klíčová slova: deep networks; automatic program synthesis; image processing Plné texty jsou dostupné v digitálním repozitáři NUŠL Transforming hierarchical images to program expressions using deep networks

We present a technique describing how to effectively train a neural network given an image to produce a formal description of the given image. The basic motivation of the proposed technique is an ...

Křen, Tomáš
Ústav informatiky, 2018

Sparse Test Problems for Nonlinear Least Squares
Lukšan, Ladislav; Matonoha, Ctirad; Vlček, Jan
2018 - anglický This report contains a description of subroutines which can be used for testing large-scale optimization codes. These subroutines can easily be obtained from the web page http://www.cs.cas.cz/~luksan/test.html. Furthermore, all test problems contained in these subroutines are presented in the analytic form. Klíčová slova: large-scale optimization; least squares; test problems Plné texty jsou dostupné v digitálním repozitáři NUŠL Sparse Test Problems for Nonlinear Least Squares

This report contains a description of subroutines which can be used for testing large-scale optimization codes. These subroutines can easily be obtained from the web page ...

Lukšan, Ladislav; Matonoha, Ctirad; Vlček, Jan
Ústav informatiky, 2018

Problems for Nonlinear Least Squares and Nonlinear Equations
Lukšan, Ladislav; Matonoha, Ctirad; Vlček, Jan
2018 - anglický This report contains a description of subroutines which can be used for testing large-scale optimization codes. These subroutines can easily be obtained from the web page http://www.cs.cas.cz/~luksan/test.html. Furthermore, all test problems contained in these subroutines are presented in the analytic form. Klíčová slova: large-scale optimization; least squares; nonlinear equations,; test problems Plné texty jsou dostupné v digitálním repozitáři NUŠL Problems for Nonlinear Least Squares and Nonlinear Equations

This report contains a description of subroutines which can be used for testing large-scale optimization codes. These subroutines can easily be obtained from the web page ...

Lukšan, Ladislav; Matonoha, Ctirad; Vlček, Jan
Ústav informatiky, 2018

A limited-memory optimization method using the infinitely many times repeated BNS update and conjugate directions
Vlček, Jan; Lukšan, Ladislav
2018 - anglický Klíčová slova: Unconstrained minimization; variable metric methods; limited-memory methods; the repeated BFGS update; global convergence; numerical results Plné texty jsou dostupné v digitálním repozitáři Akademie Věd. A limited-memory optimization method using the infinitely many times repeated BNS update and conjugate directions

Vlček, Jan; Lukšan, Ladislav
Ústav informatiky, 2018

Numerical solution of generalized minimax problems
Lukšan, Ladislav; Matonoha, Ctirad; Vlček, Jan
2018 - anglický Klíčová slova: Numerical optimization; nonlinear approximation; nonsmooth optimization; generalized minimax problems; recursive quadratic programming methods; interior point methods; smoothing methods; algorithms; numerical experiments Plné texty jsou dostupné v digitálním repozitáři Akademie Věd. Numerical solution of generalized minimax problems

Lukšan, Ladislav; Matonoha, Ctirad; Vlček, Jan
Ústav informatiky, 2018

UFO 2017. Interactive System for Universal Functional Optimization
Lukšan, Ladislav; Tůma, Miroslav; Matonoha, Ctirad; Vlček, Jan; Ramešová, Nina; Šiška, M.; Hartman, J.
2017 - anglický This report contains a description of the interactive system for universal functional optimization UFO, version 2017. This version contains interfaces to the MATLAB and SCILAB graphics environments. Klíčová slova: numerical optimization; nonlinear programming; nonlinear approximation; algorithms; software systems Plné texty jsou dostupné v digitálním repozitáři Akademie Věd. UFO 2017. Interactive System for Universal Functional Optimization

This report contains a description of the interactive system for universal functional optimization UFO, version 2017. This version contains interfaces to the MATLAB and SCILAB graphics environments.

Lukšan, Ladislav; Tůma, Miroslav; Matonoha, Ctirad; Vlček, Jan; Ramešová, Nina; Šiška, M.; Hartman, J.
Ústav informatiky, 2017

The IINC System under the ROOT Environment
Jiřina, Marcel
2017 - anglický Klíčová slova: IINC; data separation; classification; multivariate data; distance; metric Plné texty jsou dostupné v digitálním repozitáři Akademie Věd. The IINC System under the ROOT Environment

Jiřina, Marcel
Ústav informatiky, 2017